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A simple proof of a theorem of Albert


Author: M. L. Racine
Journal: Proc. Amer. Math. Soc. 43 (1974), 487-488
MSC: Primary 16A40
DOI: https://doi.org/10.1090/S0002-9939-1974-0330218-2
MathSciNet review: 0330218
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Abstract: A simple proof is given of the following theorem of Albert: An associative division algebra of degree 4 over its center is of order 4 in the Brauer group if and only if it cannot be written as a tensor product of quaternion algebras.


References [Enhancements On Off] (What's this?)

  • [1] A. A. Albert, New results in the theory of normal division algebras, Trans. Amer. Math. Soc. 32 (1930), 171-195. MR 1501532
  • [2] -, Normal division algebras of degree four over an algebraic field, Trans. Amer. Math. Soc. 34 (1932), 363-372. MR 1501642
  • [3] -, Structure of algebras, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R.I., 1939. MR 1, 99.

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DOI: https://doi.org/10.1090/S0002-9939-1974-0330218-2
Article copyright: © Copyright 1974 American Mathematical Society

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